Method for preventing deformation in a well casing

ABSTRACT

A method for preventing deformation of the casing of a well bore hole extending into a reservoir interval within a subterranean hydrocarbon-bearing earth formation wherein such deformation is caused by the compaction of the reservoir interval in which unconsolidated sand therein compacts when the fluid pressure of the interval is reduced. A core sample is extracted from the interval containing a substantially undisturbed portion of unconsolidated sand typical of that contained in the interval. The extent of vertical compressibility of the cored sample is measured relative to its orientation within the reservoir interval and its lateral confinement in the configuration it exhibits under an isostatic compressive force equaling that existing within the interval. The vertical extent of the sand contained within the interval and the extent of reservoir interval compression that would result from a vertical compression of the sand contained in the reservoir interval by an amount corresponding to the measured compressibility of the core sample are determined. The portion of the well casing to be disposed against the interval is equipped with slip couplings adapted to provide an extent of slip having a selected degree of correspondence with the predetermined extent of reservoir interval compressibility.

i efill 72] Inventors Leo P. Broussard New Orleans, La.;Leon L. Dickson,Jr.: Wilhelmus J G. Gardenier, Houston, Tex. [2]] Appl. No. 5,078 [22] Filed Jan. 22, 1970 [45] Patented May 25, 1971 [73] Assignee Shell Oil Company New York, N.Y.

[54] METHOD FOR PREVENTING DEFORMATION IN A WELL CASING 7 Claims, 6 Drawing Figs. [52] U.S. Cl 166/250, 73/34, 73/151,166/315 [51] Int. Cl E2lb,l7/08; E2lb49/02,G0ln 3/10 [50] Field of Search 166/250, 315, 242; 73/94, 151

[5 6] References Cited UNITED STATES PATENTS 2,712,854 7/1955 Creighton 166/242 2,900,028 8/1959 Hanes 166/242 166/242 3,020,962 2/1962 Holmquist 3,505,860 4/1970 Bishop etal.

ABSTRACT: A method for preventing deformation of the cats ing of a well bore hole extending into a reservoir interval within a subterranean hydrocarbon-bearing earth formation wherein such deformation is caused by the compaction of the reservoir interval in which unconsolidated sand therein corn pacts when the fluid pressure of the interval is reduced. A core sample is extracted from the interval containing a substantially undisturbed portion of unconsolidated sand typical of that contained in the interval. The extent of vertical compressibility of the cored sample is measured relative to its orientation within the reservoir interval and its lateral confinement in the configuration it exhibits under an isostatic compressive force equaling that existing within the interval. The vertical extent of the sand contained within the interval and the extent of reservoir interval compression that would result from a vertical compression of the sand contained in the reservoir interval by an amount corresponding to the measured compressibility of the core sample are determined. The portion of the well casing to be disposed against the interval is equipped with slip couplings adapted to provide an extent of slip having a selected degree of correspondence with the predetermined extent of reservoir interval compressibility.

TOPFIXED l- POINT PATENTED MAY25 |97| SHEET 1 BF 3 3580,1384

.. 4 m. fig

INVENTORSI FIG.

L.P. BROUSSARD L.L. DICKSON,JR.

W.J. G. GARDENIER THElR ATTORNEY PATENTEU HAY25I97I 3380.334

sum 2 or 3 TEMPERA CONTROLLER TEMPERATURE CONTROLLER NITROGEN IN FIG-3 74 /gz I 73 T65 82 fl/ 62 INVENTORS swi H:

THEIR ATTORNEY PATENTEUMAY25197| sum 3 BF 3 FlG.6

INVENTORS.

| P. BRQUSSARD 1.. 1.. DICKSON, JR.

W.J- G. GARDENIER BY:D?I 9 THEIR ATTORNEY METHOD FOR PREVENTING DEF ORMATION IN A WELL CASING BACKGROUND OF THE INVENTION 1. Field of the Invention The invention relates to well completion; and, more particularly, to a method for preventing buckling of a well casing adjacent to areas susceptible to compaction.

2. Description of the Prior Art In Louisiana oil fields, certain oil-bearing formations have shown a tendency to compact after substantial amounts of oil have been removed therefrom. This causes severe problems in regard to the casing and tubing in the wells extending into these formations. In bending, the cement surrounding the well casing cracks and sand is produced. Such bending is detrimental to the working of such wells since it is impossible to run tools and devices down the bent well to carry out remedial operations.

The determination of how much deformation will take place in well casings extending into such formations is important. Providing for too little slip would lead to expensive casing failures and providing for too much slip would lead to excessive installation expense.

SUMMARY OF THE INVENTION It is an object of this invention to provide a method for preventing buckling of well traversing areas susceptible to compaction.

It is a further object of this invention to provide a method for determining the extent of deformation that is to take place in a well casing extending into a reservoir interval susceptible to compaction when its fluid pressure is reduced.

These and other objects are preferably accomplished by extracting a core sample from the interval containing a substantially undisturbed portion of unconsolidated sand typical of that contained in the interval. The extent of vertical compressibility of the cored sample is measured relative to its orientation within the reservoir interval and its lateral confinement in the configuration it exhibits under an isostatic compressive force equaling that existing within the interval. The vertical extent of the sand contained within the interval and the extent of reservoir interval compression that would result from a vertical compression of the sand contained in the reservoir interval by an amount corresponding to the measure compressibili ty of the core sample are determined. The portion of the well casing to be disposed against the interval is equipped with slip coupling means adapted to provide an extent of slip having a selected degree of correspondence with the predetermined extent of reservoir interval compressibility. The method described hereinabove is applicable to any reservoir interval that contains unconsolidated said that becomes compacted when the reservoir fluid pressure is reduced. Preferably, such a method is used in conjunction with determinations of the amount of shale contained in a reservoir interval and the amount by which it will be compressed during a selected production time interval.

BRIEF DESCRIPTION OF THE DRAWING FIG. 1 is a vertical sectional, partly schematic, view of a well in accordance with the teachings of the present invention;

FIG. 2 is a vertical sectional, partly schematic, view of the well of FIG. I subject to buckling;

FIG. 3 is a schematic illustration of a method of testing a sample in accordance with the teachings of our invention;

FIG. 4 is a detail of a portion ofthe illustration of FIG. 3;

FIG. 5 is a vertical sectional, partly schematic, view of the well of FIG. I wherein the well casing is provided with slip coupling means in accordance with the teachings of the present invention; and

FIG. 6 is a vertical, partly sectional, view of the expansion joint means of FIG. 5.

Referring to the drawing, FIG. 1 shows a well borehole 10 extending into a subterranean oil-bearing formation 11. Well borehole 10 includes a casing 12 cemented therein by cementing, as at 13. Well borehole 10 may also include a tubing string 14 and a packer 15 as is well known in the art for working well borehole 10. The well casing 12 may also be perforated with perforations 16 extending through casing 12, cement l3 and into formation 11, as is well known in the art.

Oil-bearing formation 11 may, for example, be divided into an upper sand-shale area 17, a lower shale area 18, a still lower sand area 19 and a bottom shale area 20. For the purposes of this discussion, it will be assumed that oil-sand area 19 is highly susceptible to compaction. As illustrated in FIG. 1, the zone of interest, i.e., the area in which any buckling of casing 12 is likely to occur due to sand compaction, comprises a top fixed point adjacent to shale area 18 and a bottom fixed point adjacent to the bottom of sand area 19. Thus, axial load on casing 12, prior to production, is substantially negligible.

Referring now to FIG. 2, after production of well borehole 10 through perforations l6 and up tubing string 14 past packer 15, a significant amount of compaction of the sand in the oil-sand area 19 has taken place. Thus, as can be seen in FIG. 2, casing 13 cement 13 and tubing string 14 show a serious amount of buckling adjacent to sand area 19. The axial load on casing 12 is high, in the order of, for example, 560,000 to l,l00,000 pounds. The top fixed point has shifted by an amount A L to a lower fixed point. Due to the axial loads on casing 12, causing deformation takes place. Such deformation renders the working within well borehole 10 very difficult and expensive.

Such casing buckling may be prevented by cutting a section of the cemented casing 12 adjacent to the sand area 19 by means of pipe cutters or the like, well known in the art. The cut section of the casing 12 may be so cut as to destroy it for all practical purposes so that the cut pieces fall to the bottom of well borehole 10. This results in shortening the pipe string or casing in the area of compaction, thus relieving the axial stress on casing 12. After cutting, an internal sleeve may be installed between the horizontally cut sections of casing 12, alternatively, the cutaway portion may be otherwise sealed such as by injection of epoxy resin or other suitable sealing means. Nevertheless, the above operation is expensive and alignment of the two casing sections may be difficult once the casing 12 is cut or destroyed. In addition, said consolidation of sand area 19 is limited and in some cases may be impossible once the casing 12 is destroyed.

Preferably, however, in accordance with the teachings of the present invention, formation 11 is logged by techniques well known in the art so as to determine the upper and lower limits of sand area 19, i.e., the potentially productive zone. When a rock sample of a subterranean earth formation is brought to the earths surface, it undergoes isostatic expansion. Prior to the measurement of compressibilities, which are representative of reservoir conditions, the original in situ stress condition must be restored by isostatic compression. Subsequent measurement of reservoir compressibility requires lateral confinement and further compression in the vertical plane only.

For consolidated rock, this sequence of events may simply be enacted by surrounding the sample with fluid, raising the fluid pressure to the desired level and subsequently applying a vertical load by means of a piston arrangement. With unconsolidated material, however, this latter stage quickly results in shear failure as the fluid cannot keep the material in place.

However, if the sample is compressed, during the isostatic loading stage, by a vertical load transmitted by a piston and an 1 equal side load transmitted by a special fluid" through a thin sleeve of a material adapted to withstand high temperatures, such as Viton, a synthetic rubber copolymer manufactured by E. I. DuPont de Nemours and Co., and onto the sample is compressed to the desired in situ conditions, the fluid can be made to harden after which the piston may be used to further load the sample in the vertical direction. The special fluid may be any material for which volume change during hardening and compressibility after hardening are negligible. For example, an Epon saturated silicon carbide may be used, Epon being an epoxy resin manufactured by Shell Oil Company.

Referring once again to FIG. 2, when fluids are withdrawn from the zone of interest, L, a reduction takes place in the pore fluid pressure accompanied by an increase in effective stress and compaction of the reservoir rock. The compressibility of an unconsolidated sand is highly dependent on sand grain arrangement. Such arrangement must thus be closely preserved. To minimize disturbances due to handling, core sections which are extracted means well known in the art, are frozen as with dry ice, immediately upon surfacing and before removal from the core extracting means, as, for example, from a core barrel. Sample core specimens for compressibility determinations are then drilled in liquid nitrogen from the frozen core material and placed in dry ice. Before measuring their compressibilities, the grains in these samples are restored to their in situ proximity by restoring the in situ stresses.

A preferred method is to take the frozen sample specimens, thaw them under an isostatic stress of a few hundred p.s.i. and subsequently load them isostatically while measuring the resulting changes in pore volume. The plot of pore volume versus isostatic stress was found to exhibit a distinct knee" at an isostatic stress corresponding to the vertical effective stress which had been calculated from:

where:

',.= vertical effective stress S= vertical stress p pore fluid pressure as will be discussed further hereinbelow. Thus, the samples remember" their in situ effec tive stress indicating no serious grain disorientation during coring, freezing, drilling, and isostatic loading.

Referring now to FIG. 3, a schematic diagram is shown of preferred apparatus for allowing isostatic compression of unconsolidated sand samples to be followed by axial compression under lateral confinement. A compression cell 62 is shown containing a core sample 63 therein. A sleeve 64 is shown surrounding core 63. As seen in detail in FIG. 4, sleeve 64 preferably includes an inner metallic sleeve 65, such as copper foil, and an inner sleeve 66, of a material such as Viton. Porous frits 67 and 68 are disposed within cell 62 at the top and bottom of core 63, respectively. A fixed piston 69 is disposed within cell 62 above upper frit 67. A moving piston 70 is disposed within cell 62 below lower frit 68. A loading linkage 71 is connected to piston 70 for coupling cell 42 to the apparatus of FIG. 3. A passageway 72 extends through piston 70 for permitting air to escape therefrom. The space 73 directly outside the outer sleeve 66 preferably contains silicon carbide particles therein to decrease the compressibility of the cured material of sleeve 66 as will be discussed further hereinbelow. A reservoir 74, filled with the special fluid," such as Epon-saturated silicon carbide as discussed hereinabove, is disposed within the outer wall 75 of cell 62. A suitable passageway 76, normally closed by a plug 77,. is disposed in the upper wall 68 of cell 62 for introducing the Epon material into reservoir 74. In like manner, a suitable passageway 79 is disposed in upper wall 68 communicating with space 73 and normally closed by a plug 80, for introducing the silicon carbide and Epon fluid into space 73. A passageway 81 extends through piston 69 for introducing fluid into cell 62. Finally, a cleaning plug 82 may be disposed in the wall 75 of cell 62 for access to the interior thereof. Suitable bolts 83 are connected to cell 62 for coupling the cell 62 to the apparatus of FIG. 3.

Referring once again to FIG. 3, the loading linkage 71 of cell 62 is coupled to a first intensifier 84 which is in turn coupled to a second intensifier 85 through line 86. Intensifier 85 is coupled to a conventional pressure gauge 87 through line 88. Line 86 is connected to a line 89 coupled to both a conventional pressure gauge 90 and an oil supply 91 through line 92. Oil supply 91 is coupled to a nitrogen supply 93 through line 94. Liquid mercury is preferably disposed at both the oil and nitrogen supplies. A nitrogen inlet line 95 is coupled to nitrogen supply 93 for introducing nitrogen thereto.

Line 96, coupled to line 88, connects gauge 87 and intensifier 85 to cell 62 through lines 97 and 98. Line 98 is also coupled to a conventional pressure gauge 98a. A thermocouple line 99 coupled cell 62 to a temperature controller 100. Temperature controller 100 is in turn coupled to a heater 101 surrounding cell 62 through line 102. The entire apparatus is preferably housed in a suitable enclosure 103, such as a Lucite box. A second temperature controller 104 is coupled to enclosure 103 and includes a thermocouple 105 and a heater 106 for controlling the temperature within enclosure 103.

In operation, referring to FIG. 3, the core sample 62 is compressed by a vertical load transmitted by piston 70 and an equal side load transmitted by the special Epon fluid within reservoir 74 (FIG. 4) through the two thin sleeves 65 and 66 onto core sample 63. The outer sleeve 66 serves as a fluid seal while inner sleeve 65 prevents the material of sleeve 66 from flowing into the sample 63. As discussed hereinabove, the space directly outside of sleeve 66, i.e., reservoir 74, preferably contains silicon carbide particles with the Epon fluid occurring the void spaces between the particles. Preferably, this special fluid is a mixture of Epon 1031, Epon 828 and Nadic Methyl Anhydride, a curing agent, in a proportion by weight of l:l:l.8. The viscosity of this mixture prior to curing is sufficiently low for the purposes set forth herein. Thus, the Epon remains in a liquid state at room temperature, and is in contact with Epon in a storage reservoir (not shown). The pressure applied to the Epon in the reservoir may be read on pressure gauge 87 (FIG. 3) and the transmittance of pressure through the Epon may be checked by means of pressure gauge 98.

When the sample 63 has been compressed to the desired isostatic stress level at approximately room temperature, the Epon may be hardened by raising the temperature through controller 10, lines 99 and 102 and heater 101. If, for example, the sands of interest originate from reservoirs with temperatures above F., at 160 F., the Epon hardens in about two weeks'; at higher temperatures, the hardening process takes less time. Thus, by raising the temperature of sample 63 to reservoir temperature, a condition may be induced which allows subsequent axial compression under lateral confinement, and, at the same time, achieves an in situ temperature condition. After the Epon sets up, the sample is then con-- tained by solid vertical boundaries.

DETERMINATION OF SAND COMPRESSIBILITY The compressibility of formation 19 may be determined from the foregoing data. As discussed hereinabove, assuming a formation reservoir of alternating sand and shale beds and neglecting gravitational effects within the reservoir, it may be assumed that the vertical stress, s, due to the weight of the overburden and the pore fluid pressure, p, are constant throughout. The part of the vertical stress due to the overburden weight that is not carried by the pore fluid pressure o',.=Fp (l) is supported by the rock matrix. This vertical stress 0,. which is called the effective stress, is mainly responsible for the state of compaction of the rock.

Assuming that the pore fluid pressure in a sand or shale bed is decreased, with s constant, an increase in effective stress A0,.=Ap (2) and compaction of the bed is caused according to Ah/h=cAa,. (3) where h is bed thickness, and c represents the compressibility of the bed material. The compressibility is assumed constant in the effective stress rang 0',- to o' -l-Ao' In equation (3), the conditions on the vertical boundaries must be specified. Assume no horizontal movement, i.e.,

lateral confinement at every point in the reservoir, and using elastic theory, it has been discovered that, for infinite depth of burial, the compaction at the center of a reservoir approaches the compaction under conditions of lateral confinement when the ratio of the radial extend of the reservoir to its thickness (r /h) approaches infinity. For r llr=50 (e.g., radial extend 2,000 ft., total reservoir thickness 40 ft.), the compaction at the center of the reservoir is still 99 percent of the compaction under lateral confinement. It appears that, for finite depths of burial, compaction at the center of the reservoir, though frequently considerably less, is never much greater than compaction under lateral confinement. Thus, the assumption with regard to equation (3) of lateral confinement, tends to yield upper bound values for reservoir compaction.

Assuming that we have an instantaneous fluid pressure decrease in the sand, the corresponding increase in effective stress is given by equation (2), and the resulting compaction by equation (3) which in this case reads Ah/h=Azr,. (4) where Ah is the compaction of an individual sand bed or total compaction of the sand, depending on whether h represents the thickness of an individual bed or total sand thickness. For practical purposes, this compaction can be assumed to occur immediately.

In the foregoing an instantaneous and uniform pressure decrease in the sand (i.e., the pressure drop is the same throughout the entire reservoir) has been assumed. The assumption of uniformity appears reasonable when the sand permeability is high, so that pressure drawdown towards the well bore is small. Uniformity in the vertical direction implies pressure communication between the individual sand beds.

Thus, in the discussions hereinabove, the sand compressibility of the sample may be determined, by means of equation (4) above, using vertical displacements resulting from additional piston loading. The flexible sleeve 66 minimizes the reduction of the effective piston load due to friction between sample 63and the walls of reservoir 74.

An increase in vertical load results in an increase in radial stress exerted by the sample 23 of the cured Epon. The compressibility of the cured Epon has been found to be lower than that of unconsolidated sand. In addition, the presence of silicon carbide decreases the compressibility of the cured Epon when, due to some radial compression of the cured Epon itself, the silicon carbide particlesestablish closer contact allowing them to carry an increasing portion of the additional radial stress. However, with some slight horizontal movement still possible, measured sand compressibilities may be somewhat high, but the error can be expected to decrease with increasing vertical stress.

After the compressibility of the sample 63 has been determined, slip couplings are installed in casing 12 of FIGS. 1 and 2 adjacent, i.e., opposite, above or below, the interval 19. Such slip couplings are placed and are of such a length so as to provide an extent of slip having a selected degree of correspondence with the predetermined extent of reservoir interval compressibility. Thus, as shown in FIG. 5, a first slip coupling 21 is shown disposed adjacent the base of sand area 19.

Although two such slip couplings are shown in FIG. 5, obviously one or more couplings may be installed in the well casing 12 within the well borehole 10. Also, as is well known in the art, short sections in a string of pipe or casing, known as subs," may be installed in a well casing. Here, the sub is the slip coupling which, as will be discussed further hereinbelow with reference 'to FIG. 4, is a telescoping section in the casing 12. The subs" (i.e., couplings 21 and 22) are disposed adjacent to sand area 19 which is susceptible to compaction. If necessary to assure the proper location of couplings 21 and 22 in the well borehole with respect to the productive zone or zones, such as sand area 19, a collar locator log, as is well known in the art, may be taken prior to cementing the casing 12 in place. After the appropriate slip coupling or couplings are installed, casing 12 is cemented and the productive zones,

such as sand area 19, are perforated in a conventional manner, as at perforations 16 with appropriate sand consolidation techniques being applied, where applicable. Pattern perforating for use with more sophisticated sand consolidation placement tools may be effected in a conventional manner as the coupling or couplings do not reduce drift through the casing 12. Thus, as seen in FIG. 5, axial loads induced on casing 12 by compaction of sand area 19 between fixed casing points and by packer forces and/or other forces associated with conventional oil well production practices, are absorbed by slip couplings such as couplings 21 and 22, thus precluding buckling of casing 12. Although only one such sand area susceptible to compaction has been shown, obviously a plurality of such vertically spaced areas or strata may be traversed by well borehole 10 with appropriate slip couplings installed as required.

Referring now to FIG. 6, a slip coupling in accordance with the teachings of this invention is illustrated. Obviously, all the slip couplings may be similar to slip coupling 21 illustrated in FIG. 6 and described hereinbelow.

Slip coupling 21 includes an inner member 23 slidably mounted in an outer member 24. Thus, member 23 telescopes into member 24. The upper end of inner member 23 includes a threaded portion 25 for connecting coupling 2l to a standard casing coupling (not shown). In like manner, the lower end of outer member 24 includes a like threaded portion 26 for connecting coupling 21 to a standard casing coupling (not shown). In this manner, the slip coupling 21 may be connected at any desired location in casing 12.

Inner member 23 includes an outer circumferential skirt portion such as cylinder 27, preferably of steel or similar material adapted to extend downwardly into a chamber 28, also preferably of steel, extending circumferentially of outer member 24. Cylinder 27 maybe threaded onto the outer wall of inner member 23 as indicated by threads 29; alternatively, cylinder 27 may be integral with inner member 23, if desired. In either case, the outer surface of cylinder 27, adapted to slide downwardly into chamber 28, is coated to prevent cement bonding of the inner member 23 in chamber 28. Suitable bonding materials may include a pliable rubber sleeve, rubber base material, etc.

A slot 30 extends longitudinally of cylinder 27. A pin 31 fixed in position in chamber 28 is adapted to slidably engage slot 30 so as to prevent rotation and/or premature movement of inner member 23 with respect to outer member 24. Obviously, a plurality of such pins and mating slots may extend circumferentially of chamber 28 and cylinder 27, respectively.

The upper movement of cylinder 27 with respect to chamber 28 is limited by stop means 32 on cylinder 27 adapted to engage mating stop means 33 in chamber 28. A plurality of O-rings seal cylinder 27 and chamber 28 so as to exclude debris from the coupling 21. If desired, chamber 28 may comprise an integral member, or, as shown in FIG. 6, be formed of sections threaded to outer member 24 as at threads 34 and 35, respectively, to form an integral chamber for cylinder 27 A bellows 36 is disposed in chamber 28, fixed at one end 37 by brazing or other means well known in the art on cylinder 27 and the other end 38 to an abutment wall 39 disposed at the lower end or bottom of chamber 28. Bellows 36 provides a pressure seal between inner member 23 and outer member 24. Bellows 36 is preferably of a thin-walled multi-ply material resistant to corrosion, such as monel metal. The sealed bellows chamber, that is, the portion of chamber 28 between cylinder 27 and abutment wall 39, is preferably filled with a noncompressible fluid, such as oil, to prevent well bore fluids such as mud or cement from obstructing bellows movement and to lubricate the cylinder and chamber walls.

A pair of valve chambers 40 and 41 are disposed below abutment wall 39. Ports 42 and 43, respectively, lead from the bellow chamber to the respective chambers 40 and 41. Springloaded check valves disposed in chambers 40 and 41, respectively, with springs 46 and 47, respectively, fixed at one end to their respective valve and the other end to the bottom wall of their respective chambers. Relief ports 48 and 49 are formed in chambers 40 and 41, respectively, for allowing displacement of the noncompressible chamber fluid when movement of casing 23 occurs due to axial loading as discussed hereinabove.

Conventional piston-type equalizers, such as equalizer 50, to provide for the internal pressure within the bellows chamber are preferably disposed in an equalizer chamber 51 below abutment wall 39. An outlet port 52 connects chambers 51 with the inner bellows chamber and an inlet port 53 is disposed at the lower end of the chamber 51. A similar arrangement is utilized to provide for the external pressure within the bellows chamber. In this equalizer chamber (identical to 51 except for ports) an outlet port 61 connects the equalizer chamber with the outer bellows chamber and an inlet port 60 is disposed at the lower end of the equalizer.

chamber. The purpose of the pressure equalizer is to equalize the pressure on either side of the bellows with respective pressures outside and inside the casing 24 without allowing external fluid, such as cement, to enter the sealed bellow chamber.

Thus, in operation, as illustrated in FIG. and discussed hereinabove, as axial load is placed on casing 12 as a result of compaction of the sand in sand area 19, slip couplings 21 and 22, previously installed in casing 12 by means of treads 25 and 26, respectively, provide a mechanical means for relieving axial loads on casing 12, thus providing a maximum chance for sand consolidation and a minimum chance for complicated and expensive workovers, especially offshore, associated with casing deformation due to buckling.

Thus, as the casing 12 is disposed to buckle due to axial stress, inner member 23 of slip coupling 21 telescopes downwardly into outer member 24 while maintaining a seal therebetween due to O-rings 34. Pin or pins 31 slide in a slot or slots 31, thereby preventing rotation and/or premature movement between members 23 and 24. Bellows 36 provides a high pressure seal, thereby permitting installation of like couplings opposite all potentially productive zones in formation 11 along with a minimum chance of casing leakage. Such a leakproof connection in a producing zone is important so as to prevent excessive gas production from the top of the producing zone and water production from the base of the producing zone. Check valves 44 and 45, along with equalizer 50, provide an appropriate integral relief system allowing displacement of the noncompressible chamber fluid when casing movement occurs.

In summary, the slip couplings of the present invention, properly installed in well casing and of a length in accordance with the determination of the compressibility of the formation as discussed hereinabove, provide casing relief with minimum resistance adjacent to formations susceptible to compaction. The external coating of the upper cylinder 27 prevents cement adhesion and the oil-filled/sealed bellows chamber excludes cement and other foreign material. The low resistance to movement offered by the bellows 36, preferably multi-ply, and the oil-lubricated cylinder and chamber walls insures minimum resistance to movement with maximum relief of axial casing loads.

ln completing a field scale pattern of wells into the same reservoir interval, the method of our invention may be used on each well, with measurement information obtained from cores or logs of one well containing a typical portion of the sand being used to determine the extent of travel for the slip couplings to be used in other wells.

We claim:

1. A method for preventing deformation of the casing of a well borehole extending into a reservoir interval within a subterranean hydrocarbon bearing earth formation, the deformation being caused by the compaction of the reservoir interval in which unconsolidated sand therein compacts when the fluid pressure of the reservoir interval is reduced, said method comprising the steps of:

extracting a core sample from said interval containing a substantially undisturbed portion of unconsolidated sand typical of that contained in the reservoir interval; measuring the extent of the vertical compressibility of the cored sand sample relative to its orientation within the reservoir interval and its lateral confinement in the configuration it exhibits under an isostatic compressive force equaling that existing within the reservoir interval;

determining the vertical extent of said sand that is contained within the reservoir interval;

determining the extent of reservoir interval compression that would result from a vertical compression of the sand contained in the reservoir interval by an amount corresponding to the measured compressibility of the core sample; and

equipping the portion of said well casing to be disposed adjacent said reservoir interval with slip coupling means adapted to provide an extent of slip having a selected degree of correspondence with the predetermined extent of reservoir interval compressibility.

2. The method of claim 1 including the step of fixing said casing firmly in position in said well borehole after equipping said well with said slip coupling means.

3. The method of claim 1 wherein the step of providing said well casing with slip coupling means including providing said casing with at least one slip coupling means disposed adjacent to substantially the top of the'interval susceptible to compaction and at least one slip coupling means disposed adjacent to substantially the bottom of the interval susceptible to buckling.

4. The method of claim 1 wherein the step of measuring the extent of vertical compressibility of the sample comprises the step of placing both a vertical load and a side load equal in pressure on said sample, said vertical load being carried out by a piston and said side load being carried out by a fluid of a hardenable material adapted to withstand high temperatures.

5. The method of claim 4 wherein the step of placing a side load using a fluid includes the step of applying epoxy resinsaturated silicon carbide to said sample.

6. The method of claim 1 wherein the step of measuring the extent of vertical compressibility of the sample comprises the steps of:

placing both a vertical load and a side load equal in pressure on said sample;

increasing the pressure on said sample; and

measuring the pressure at each increment of pressure on said sample.

7. The method of claim 6 including the step of detennining the compressibility of said sample from the following equation where Ah is the compaction of the core sample;

h is the thickness of the core sample;

0 is the compressibility of the core sample; and

A0,. is the increase in effective stress of the core sample. 

2. The method of claim 1 including the step of fixing said casing firmly in position in said well borehole after equipping said well with said slip coupling means.
 3. The method of claim 1 wherein the step of providing said well casing with slip coupling means including providing said casing with at least one slip coupling means disposed adjacent to substantially the top of the interval susceptible to compaction and at least one slip coupling means disposed adjacent to substantially the bottom of the interval susceptible to buckling.
 4. The method of claim 1 wherein the step of measuring the extent of vertical compressibility of the sample comprises the step of placing both a vertical load and a side load equal in pressure on said sample, said vertical load being carried out by a piston and said side load being carried out by a fluid of a hardenable material adapted to withstand high temperatures.
 5. The method of claim 4 wherein the step of placing a side load using a fluid includes the step of applying epoxy resin-saturated silicon carbide to said sample.
 6. The method of claim 1 wherein the step of measuring the extent of vertical compressibility of the sample comprises the steps of: placing both a vertical load and a side load equal in pressure on said sample; increasing the pressure on said sample; and measuring the pressure at each increment of pressure on said sample.
 7. The method of claim 6 including the step of determining the compressibility of said sample from the following equation Delta h/h c Delta sigma v where Delta h is the compaction of the core sample; h is the thickness of the core sample; c is the compressibility of the core sample; and Delta sigma v is the increase in effective stress of the core sample. 